Finite Group Databasebeta

← C2×#13074467 #14920480

Subgroups — C2×#13074467 #14920480

Order 2816.

3670 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13074467C2116yesmaximal, direct product factor
4C2×#10622287C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622560C212yesmaximal, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622833C212yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C24×Dic11C2212yes—
18C23×Dic22C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×D4×Dic11—28no—
26C2×D4×Dic11C2218yescomplemented
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66938—28no—
33C2×#66938C2218yescomplemented
34C11×#392C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36#10622836C22116yescomplemented
37#10622836C2218yescomplemented
38#10622833C22116yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622571C22116yescomplemented
45#10622566C2218yescomplemented
46#10622560C22116yescomplemented
47#10622287C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C24×D11C2311yescharacteristic
52C22×D4×C11—28no—
53C22×D4×C11—28no—
54C22×D4×C11—24no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—28no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2318yes—
69C23×Dic11—28no—
70C23×Dic11—44no—
71C23×Dic11—44no—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2318yes—
78C22×Dic22—24no—
79C22×Dic22—44no—
80C22×Dic22C2314yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—44no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—44no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93D4×Dic11—232no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11C2314yes—
102C2×C4×Dic11D418yescomplemented
103C2×C4×Dic11C2314yes—
104#66938—232no—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2631—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11—22no—
123C24×C11#4118yes—
124C24×C11C2412yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C23×D11—22no—
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—22no—
132C23×D11C2412yes—
133C2×D4×C11—232no—
134C2×D4×C11—216no—
135C2×D4×C11—216no—
136C2×D4×C11—28no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—432no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—432no—
156C2×C22⋊D11—416no—
157C22×Dic11—216no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—48no—
170C22×Dic11—48no—
171C22×Dic11—432no—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C2×Dic22—28no—
180C2×Dic22—48no—
181C2×Dic22—416no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—48no—
184C22⋊Dic11—28no—
185C22⋊Dic11—216no—
186C22⋊Dic11—48no—
187C22⋊Dic11—48no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191C4⋊Dic11—28no—
192C4×Dic11C2×D4116yescomplemented
193C22×#124—111no—
194C22×C4×D4—111no—
195#2631—1116no—
196C2×#397—111no—
197C2×#397—111no—
198C2×#393—112no—
199C2×#392—112no—
200C2×#392—111no—
201C2×#392D1111yescharacteristic, complemented
202C2×#386—112no—
203C2×#386—112no—
204C2×#383—111no—
205C23×C11—216no—
206C23×C11—216no—
207C23×C11—216no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11C22×D412yes—
229C23×C11C2×#4118yes—
230C23×C11C2×#4114yes—
231C23×C11H(5,𝔽2)14yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)12yes—
234C23×C11C2511yescharacteristic
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—22no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—48no—
244C22×D11—48no—
245D4×C11—232no—
246D4×C11—432no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—44no—
255C2×C4×C11—48no—
256C2×C4×C11C22×D414yes—
257C22⋊D11—416no—
258C22⋊D11—432no—
259C2×Dic11—28no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—432no—
273C2×Dic11—44no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276C2×Dic11C22×D414yes—
277C2×Dic11C22×D414yes—
278Dic22—416no—
279C23×Q8—111no—
280C23×D4—111no—
281C23×D4—112no—
282C23×D4C2×D1111yescharacteristic
283C23×D4C2×D1112yes—
284C24×C4—112no—
285C2×#124—118no—
286C2×#124—228no—
287C2×C4×D4—118no—
288C2×C4×D4—228no—
289C22×C4⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4C2×D1112yes—
299C22×C42—111no—
300#397—118no—
301#397—118no—
302#393—1116no—
303#392—1116no—
304#392—118no—
305#392C2×D1118yescomplemented
306#386—1116no—
307#386—1116no—
308#383—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C22×C11—28no—
316C22×C11—28no—
317C22×C11—28no—
318C22×C11—432no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—88no—
329C22×C11#52514yes—
330C22×C11#53514yes—
331C22×C11#53514yes—
332C22×C11#53818yes—
333C22×C11#53818yes—
334C22×C11C23×D411yescharacteristic
335C22×C11C22×#4112yes—
336C22×C11C2×H(5,𝔽2)12yes—
337C22×C11C2×H(5,𝔽2)11yescharacteristic
338C22×C11C2×H(5,𝔽2)11yescharacteristic
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—88no—
345C4×C11—24no—
346C4×C11—42no—
347C4×C11—44no—
348Dic11—24no—
349Dic11—24no—
350Dic11—42no—
351Dic11—44no—
352Dic11—44no—
353C25—111no—
354C25C22×D1111yescharacteristic
355C25C22×D1112yes—
356C22×Q8—114no—
357C22×Q8—224no—
358C22×Q8—444no—
359C22×D4—28no—
360C22×D4—28no—
361C22×D4—24no—
362C22×D4—44no—
363C22×D4—44no—
364C22×D4—114no—
365C22×D4—118no—
366C22×D4—224no—
367C22×D4—228no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4C22×D1114yes—
372C22×D4C22×D1118yes—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—112no—
378C23×C4—118no—
379C23×C4—228no—
380C23×C4—444no—
381C23×C4—444no—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385#124—2232no—
386C4×D4—2232no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—224no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—444no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4C22×D1114yes—
406C2×C22⋊C4C22×D1118yes—
407C2×C42—118no—
408C2×C42—114no—
409#95—118no—
410#95—118no—
411#95—114no—
412#95—118no—
413#95—118no—
414#95C22×D1114yes—
415C2×C11—48no—
416C2×C11—82no—
417C2×C11#263118yescomplemented
418C2×C11C2×#52511yescharacteristic
419C2×C11C2×#53511yescharacteristic
420C2×C11C2×#53511yescharacteristic
421C2×C11C2×#53812yes—
422C2×C11C2×#53812yes—
423D11—82no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—22no—
435C24—112no—
436C24—222no—
437C24—224no—
438C24—222no—
439C24—224no—
440C24—222no—
441C24#434118yes—
442C24C23×D1112yes—
443C24C23×D1114yes—
444C24C23×D1111yescharacteristic
445C2×Q8—228no—
446C2×Q8—448no—
447C2×Q8—4416no—
448C2×D4—232no—
449C2×D4—216no—
450C2×D4—216no—
451C2×D4—28no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—432no—
455C2×D4—228no—
456C2×D4—2216no—
457C2×D4—448no—
458C2×D4—448no—
459C2×D4—448no—
460C2×D4—4416no—
461C2×D4—4432no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—114no—
475C22×C4—2216no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—4432no—
490C22×C4D4×D1114yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1112yes—
493C22×C4C23×D1112yes—
494C4⋊C4—228no—
495C22⋊C4—28no—
496C22⋊C4—48no—
497C22⋊C4—228no—
498C22⋊C4—2216no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C42—1116no—
505C11C2×#263111yescharacteristic, complemented, Sylow
506C23—216no—
507C23—216no—
508C23—216no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—24no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—48no—
524C23—44no—
525C23—44no—
526C23—48no—
527C23—44no—
528C23—48no—
529C23—222no—
530C23—224no—
531C23—222no—
532C23—224no—
533C23—222no—
534C23—444no—
535C23—444no—
536C23—448no—
537C23—444no—
538C23—448no—
539C23C2×D4×D1112yes—
540C23C2×#434118yes—
541C23C2×#434114yes—
542C23#6703714yes—
543C23#6703712yes—
544C23#6704212yes—
545C23C24×D1111yescharacteristic
546Q8—4416no—
547D4—232no—
548D4—432no—
549D4—4416no—
550D4—4432no—
551C2×C4—28no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—114no—
561C2×C4—114no—
562C2×C4—228no—
563C2×C4—228no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—4432no—
576C2×C4—444no—
577C2×C4—448no—
578C2×C4—448no—
579C2×C4C2×D4×D1114yes—
580C22—28no—
581C22—28no—
582C22—28no—
583C22—432no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—88no—
594C22—442no—
595C22—442no—
596C22—444no—
597C22—444no—
598C22—442no—
599C22—888no—
600C22#1062311714yes—
601C22#1062312418yes—
602C22#1062313814yes—
603C22#1062314818yes—
604C22#1062324614yes—
605C22C22×D4×D1111yescharacteristic
606C22C22×#434112yes—
607C22C2×#6703712yes—
608C22C2×#6703711yescharacteristic
609C22C2×#6704211yescharacteristic
610C4—24no—
611C4—42no—
612C4—44no—
613C4—224no—
614C4—224no—
615C4—442no—
616C4—444no—
617C4—444no—
618C2—48no—
619C2—82no—
620C2—882no—
621C2#1307446718yesdirect product factor
622C2C2×#1062311711yescharacteristic
623C2C2×#1062324611yescharacteristic
624C2C2×#1062313811yescharacteristic
625C2C2×#1062312412yes—
626C2C2×#1062314812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13074467C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622560C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#392C2semidirect
26. C2×D4×Dic11C22semidirect
33. C2×#66938C22semidirect
34. C11×#392C22semidirect
36. #10622836C22semidirect
37. #10622836C22semidirect
38. #10622833C22semidirect
44. #10622571C22semidirect
45. #10622566C22semidirect
46. #10622560C22semidirect
47. #10622287C22semidirect
48. #10622264C22semidirect
102. C2×C4×Dic11D4semidirect
192. C4×Dic11C2×D4semidirect
201. C2×#392D11semidirect
305. #392C2×D11semidirect
417. C2×C11#2631semidirect
505. C11C2×#2631semidirect
621. C2#13074467direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669382
C22×D4×Dic112
#130744672
C2×#106222872
C2×#106225662
C2×#106225602
C2×#106228362
C2×#106228332
C2×#106225712
C2×#106222642
C2×C11×#3922
C2×#263111